Context. Forty years of lunar laser ranging (LLR) data provide an
excellent basis to determine various parameters of the Earth-Moon system as well as
parameters related to gravitational physics.

Aims. We update the Institut für Erdmessung (IfE) LLR model taking the
effect of a fluid lunar core into consideration. The temporal variation in the
gravitational constant Ġ/G0 and the strong
equivalence principle, parameterized by the Nordtvedt parameter η, are
investigated.

Methods. A set of LLR observations from 1970 to 2009 was analysed and
the parameters were determined by a least squares adjustment in two runs. After solving
for classical Newtonian parameters (e.g. initial conditions for the lunar orbit and
rotation) in the first run, relativistic parameters were determined in the second run.

Results. The upper limits to the gravitational constant and the
Nordtvedt parameter were found to be
Ġ/G0 = (−0.7 ± 3.8) × 10-13 yr-1
and η = (−0.6 ± 5.2) × 10-4.

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